SOLUTION: Heather's boat has a top speed of 6 miles per hour in still water. While traveling on a river at top speed, she went 10 miles upstream in the same amount of time she went

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Question 1046114: Heather's boat has a top speed of
6
miles per hour in still water. While traveling on a river at top speed, she went
10
miles upstream in the same amount of time she went
30
miles downstream. Find the rate of the river current.

Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the speed of the curent in mi/hr
+6+-+c+ = her speed going upstream
+6+%2B+c+ = her speed going downstream
Let +t+ = her time in hrs for both trips
---------------------------------------
Going upstream:
(1) +10+=+%28+6-c+%29%2At+
Going downstream:
(2) +30+=+%28+6%2Bc+%29%2At+
---------------------
(1) +t+=+10%2F%28+6-c+%29+
Plug (1) into (2)
(2) +30+=+%28+6%2Bc+%29%2A%28+10+%2F+%28+6+-+c+%29+%29+
(2) +30%2A%28+6-c+%29+=+10%2A%28+6+%2B+c+%29+
(2) +180+-+30c+=+60+%2B+10c+
(2) +40c+=+120+
(2) +c+=+3+
The rate of the current is 3 mi/hr
----------------------------------
check:
(1) +10+=+%28+6-c+%29%2At+
(1) +10+=+%28+6-3+%29%2At+
(1) +10+=+3t+
(1) +t+=+10%2F3+
and
(2) +30+=+%28+6%2Bc+%29%2At+
(2) +30+=+%28+6%2B3+%29%2At+
(2) +30+=+9t+
(2) +t+=+10%2F3+
OK

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
boat has a top speed of 6 miles per hour in still water.
While traveling on a river at top speed, she went 10 miles upstream in the same amount of time she went 30 miles downstream.
Find the rate of the river current.
:
let c = the rate of the current
then
(6-c) = effective speed upstream
and
(6+c) = effective speed downstream
:
Write a time equation; time = dist/speed
:
time up = time down
10%2F%28%286-c%29%29 = 30%2F%28%286%2Bc%29%29
cross multiply
10(6+c) = 30(6-c)
distribute
60 + 10c = 180 - 30c
10c + 30c = 180 - 60
40c = 120
c = 120/40
c = 3 mph is the rate of the current
:
:
:
Check this; find the actual time each way
10/(6-3) = 3.33 hrs
30/(6+3) = 3.33 hrs